19 19 25 triangle

Acute isosceles triangle.

Sides: a = 19   b = 19   c = 25

Area: T = 178.8643600266
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 48.86604895851° = 48°51'38″ = 0.85327764174 rad
Angle ∠ B = β = 48.86604895851° = 48°51'38″ = 0.85327764174 rad
Angle ∠ C = γ = 82.27990208298° = 82°16'44″ = 1.43660398188 rad

Height: ha = 18.82877473964
Height: hb = 18.82877473964
Height: hc = 14.30990880213

Median: ma = 20.06986322404
Median: mb = 20.06986322404
Median: mc = 14.30990880213

Inradius: r = 5.67882095322
Circumradius: R = 12.61443608686

Vertex coordinates: A[25; 0] B[0; 0] C[12.5; 14.30990880213]
Centroid: CG[12.5; 4.77696960071]
Coordinates of the circumscribed circle: U[12.5; 1.69547271527]
Coordinates of the inscribed circle: I[12.5; 5.67882095322]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.1439510415° = 131°8'22″ = 0.85327764174 rad
∠ B' = β' = 131.1439510415° = 131°8'22″ = 0.85327764174 rad
∠ C' = γ' = 97.72109791702° = 97°43'16″ = 1.43660398188 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 19 ; ; b = 19 ; ; c = 25 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 19+19+25 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-19)(31.5-19)(31.5-25) } ; ; T = sqrt{ 31992.19 } = 178.86 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 178.86 }{ 19 } = 18.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 178.86 }{ 19 } = 18.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 178.86 }{ 25 } = 14.31 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 19**2-19**2-25**2 }{ 2 * 19 * 25 } ) = 48° 51'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-19**2-25**2 }{ 2 * 19 * 25 } ) = 48° 51'38" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-19**2-19**2 }{ 2 * 19 * 19 } ) = 82° 16'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 178.86 }{ 31.5 } = 5.68 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 48° 51'38" } = 12.61 ; ;




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